Symmetrical object won't rotate on axis evenly
Set Pivot Point to Median Point


Go to Edit Mode and select vertices in the middle that creates a circle so your pivot point is now at the exact center, something like at this screen:


Press ShiftS > Cursor to Selected to move the 3D cursor to that pivot point


Now exit from Edit Mode and set the object's origin to the 3D cursor by pressing the best shortcut in the universe CtrlAltShiftC, select Origin to 3D Cursor






Whole process demonstrated on your model: